stat mech Flashcards
zeroth law
if A and B are in equilibrium and B is in equilbrium with c then A and C are in equilibrium
first law
work is a state function - the work required to go between states is independent of path
adiabatic expansion
no heat - pressure and volume change, temp doesn’t
heat capacity
partial of heat with respect to Temp at constant V or P
Ideal gas law using heat capacities
Cp-Cv = PV/T = Nkb
second law
there cannot be complete conversion of heat to work
draw a pv diagram
adiabatic and isotherm curve
adiabatic curve solution
PV^gamma for gamm=5/3
entropy equation
dQ = TdS S= kb ln(omega)
what equaitno is implied by the first law
dE = dQ+dW
enthalpy
cp = dH/dT``
Helmholtz free energy
F = E-TS
–isothermal transformations with no work
Gibbs free energy
–isothermal transformation with constant external work
G = E-TS-W
extensive, fundamental thermo equation
dE = TdS+Fdx+mudN
maxwell relations
these follow from the commutative rule of derivatives and give relations between the partial derivates at a constant variable to another (based on fund..eq)
How to find stable points
minimum of U or minimum of enthalpy (H= U-Fx) if there is an external force
Third law
The entropy of all systems at absolute zero can be taken as the universal constant= zero
Liouvilles theorem
phase space density behave like an incompressible fluid, {A,B} = -{B,A}
microcanonical ensemble
mechanically and adiabatically isolated
macrostate M=(E,x)
omega = int(dE1*exp(S1(E1)-S2(E-E1)/kb)
two-level system
H = eN, where N is number of excited impurities
Omega = N!/N1!/(N-N1)!
1/T = dS/dE at constant N , then solve for E
energy of an ideal gas with f degrees of freedom
E = (f/2)*(NkT)
canonical ensemble
temperature of the system is known - it has a resevoir from which to draw heat - no external work - uses the partition function Z =sum_u exp(-BH(u))
Gibbs canonical ensemble
Heat and work are allowed
no chemical work
Z = sum_(u,x) exp(BJ.x-BH(u))
G = -kbTln(Z)
grand canonical ensemble
chemical work and heat
no mechanical work
Z = sum_(u) exp(BuN(u)-BH(u))
Which two ensembles are identical in the thermodynamic limit
canonical and microcanonical
explain phase transitions
exist only in the thermodynamic limit (N=>infinity)
critical points = correspond to singularities in free energy
first order are discontinuous - lines separating phases
second order are continous - like past the critical point for ice
monte carlo simulations
better explanation
brownian motion
188 in kardar field
